Question

Suppose Peter has $800,000 to spend on a house and “other goods” (denominated in dollars). The price of 1 square foot of housing is $300, and Peter chooses to purchase a house of 2,000 square feet in size. Assume that houses do not differ in quality: their price is solely determined by their size. Also, assume throughout that Peter spends money on housing solely for its consumption value, not as part of his investment strategy, and that Peter has well-behaved, strictly convex preferences.

(a) On a graph with “square feet of housing” on the horizontal axis and “other goods” on the vertical axis, illustrate Peter’s budget constraint and Peter’s optimal bundle A.
(b) After Peter has bought the house, the price of housing falls to $200 per square foot. Given that Peter can sell his house from bundle A if he wants to, is Peter better or worse off? Illustrate Peter’s new budget constraint on the graph.
(c) Assuming Peter can easily buy and sell houses, will Peter now buy a different house? If so, is Peter’s new house smaller or larger than his initial house?
(d) Suppose that, instead of the price of housing dropping to $200 as in (b), the price of housing increases to $350 instead. Is Peter now better or worse off? If Peter can easily buy and sell houses, will Peter now buy a different house? If so, is Peter’s new house smaller or larger than his initial house?

Answer 1

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